The scaling in the DSTAda algorithm we propose maintains the proportion of the learning rate of each component to a greater extent in the transition process than the clipping. Its transition process is relatively smooth and stable. At the same time, clipping requires two boundary functions \(\displaystyle \eta _{l}\)  and \(\displaystyle \eta _{u}\) , but only one scaling function is needed in the DSTAda algorithm. Through the construction of \(\displaystyle {\eta _{l}}/{\eta _{u}}\) , it can be known that the constant learning rate \(\displaystyle \alpha ^{*}\)  has high degree of coupling to the upper and lower boundaries. The performance of the algorithm depends heavily on the learning rate of the stochastic gradient descent[1]}. At the same time, all the elements in the effective learning step use the same bound[2]}. It can be seen that the degree of coupling of DSTAda algorithm is low because adaptive learning rate and constant learning rate are separate and independent. It is able to adjust the adaptive learning rate \(\displaystyle {\varphi _{\rm {1}}}\left( {1/\sqrt{{v_t}} } \right)\)[3]}, [4]}, [5]}and the learning rate \(\displaystyle {\varphi _{\rm {2}}}\left( {LR} \right)\)  [6]}, [7]}, [8]}, [9]} of the stochastic gradient descent more flexibly. Adopting different learning rate strategies will have less mutual influence.
